Tony Abbott thinks giving Australians a say on same-sex marriage via the post would be a better alternative to a parliamentary vote.
But the former prime minister queries how much real authority a postal plebiscite would have.
His federal Liberal colleague Peter Dutton has pushed the case for a postal plebiscite, saying he would like the issue resolved in this term of parliament.
"I certainly think that will be better, much better, than just trying to ram this thing through the parliament," Mr Abbott told 2GB's Ray Hadley on Monday.
Having a vote in parliament - as Labor wants - would be a breach of faith with voters because the coalition didn't agree to one before the 2016 election, he said.
Mr Abbott conceded a postal plebiscite was an alternative given Labor's unwillingness to hold a formal poll.
"Here you have Bill Shorten yesterday demanding a referendum on four-year (federal) terms but is unwilling to let the people have their say on any change to the Marriage Act," he said.
A move to four-year terms requires a change to the constitution through a referendum.
Deputy Prime Minister Barnaby Joyce echoed Mr Abbott's view, insisting the issue could have been off the agenda if Labor had agreed to a policy the coalition successfully took to the election.
"If people want a discussion about a postal plebiscite, I'm happy to have that discussion," he told reporters in Canberra.
But Mr Joyce said while it matters to a section of the community, the issue was not being discussed between the vast majority of Australians.
Labor frontbencher Jason Clare agreed with Mr Dutton the issue needs to be resolved, but he called on the coalition to use the parliament not Australia Post.
"Just grow a pair. Put the legislation into the parliament and let's bloody well vote for it," he told Sky News.